Homotopy comultiplications on the localization of a wedge of spheres and Moore spaces

For an abelian group $G$ and a positive integer $n$, we set $M(G,n)$ as a Moore space of type $(G,n)$. In this paper, for a prime number $p$, we are interested in the structure of homotopy comultiplications on the localization $L_{(p)}$ of a wedge $L:={\mathbb{S}}^m\vee M(G,n)$ of the homotopy spheres and the Moore spaces for $2\le m<n$. We also provide a list of examples to examine the phenomena of homotopy comultiplications on $L_{(p)}$.